Electricity, coal, gas and climate change

Coal or Sun?  (Sundance coal-fired power plant)
Sun or Coal? – Sundance coal-fired power plant in Alberta, Canada.

It is much cleaner to produce electricity with natural gas turbines than in coal-fired power plant. This axiom supports the claim that switching from coal to gas is a solution climate change. Is it true? There must some scientific, quantitative method to verify this statement.  Let’s do some (Grade 6) math….

If you yawn at number crunching and prefer to go directly to the conclusions,  here are the key findings.

Gas well out of control North BC
Gas well out of control in Northeastern  BC.  (CBC)

Combustion formula

(1) The chemical reactions coal and gas are respectively:

  • Coal:  C + O2 → CO2 + heat (27 MJ/kg)
  • Nat Gas:  CH4 + 2 O2 →  CO2 + 2 H2O + heat (43 MJ/kg)

(2) The atomic weight of the elements :

  • Hydrogen: H : 1
  • Carbon: C : 12
  • Oxygen: O : 16
  • CO2 : 12 + 32  = 44
  • CH4 : 12 + 4 =16

(3) The ratio to CO2 are (table 1)

MoleculeFormulaRatio CO2/Fuel
Carbon CC+O2 =>CO244/12= 3.67
Methane CH4CH4 +2O2=>CO2+2H2044/16= 2.75

Table 1 means that

  • Coal : the combustion of 1 kg of carbon produces 3.67 kg CO2.
  • Nat gas : the combustion of 1 kg of nat gas produces 2.75 kg CO2.

Natural gas has a lower CO2 emission factor than carbon, thanks to the extra hydrogen molecules that produces water instead of CO2, giving also an additional combustion energy.

(4) The specific combustion heat values  are:

FuelSpecific BTUMJ/kgkWh(heat)/kg
Coal12,000 (BTU/lb)27.77.69
Natural Gas1,000 (BTU/cf)46.5712.94

GHG Emissions from fuel

(5) Assuming coal carbon concentration of 65%  (in eia range *) and 100% of methane in gas, the above CO2 emission factors become:

  • Coal: 3.67 * 0.65 = 2.38 kgCO2/kg coal
  • Gas: 2.75 * 1 = 2.75 kgCO2/kg NatGas

( * Bituminous: Containing the widest range of carbon content (45% to 86%), bituminous is mainly used as a fuel to generate electricity, though some is used as coking coal to produce steel. The oldest and most abundant coal type found in the United States, bituminous coal makes up 45% of U.S. coal production by weight and 54% by energy intensity. West Virginia leads production, followed by Kentucky and Pennsylvania.- eia)

(6)  Dividing  (5) by (4) gives CO2 emission factor per unit of energy (heat value of the fuel)

Fuel kgCO2/MJkgCO2/kWh(heat)
Natural Gas0.0590.213

The factors above are for the production of heat only from coal or gas. Extracting mechanical energy and then electrical energy from that heat implies additional energy losses.

First,  there is a limit based on the laws of thermodynamics, known since the 19th century as the Carnot theorem, directly related to the difference of temperature between the steam/hotgas and the cooling system.

η = 1- Tc/Th (Tc: Absolute temperature of the cold side, Th: Abs. temp of the hot side (Fig 1)

Thermodynamic Cycle
Fig. 1 Thermodynamic Cycle

For example,  a typical steam engine using superheated steam at 300 Deg C and cooling water at 20 Deg C, has a maximum efficiency of:

ηmax = 1 – (273+20)/(273+300) = 48.8%  i.e. regardless of any other parameter of the plant, f.ex equipment  efficiency or steam boiler vs gas  turbine, the efficiency of the system cannot exceed 48.8%. In other terms, half of the original energy in the combustible is lost in the cooling tower. (reason why co-gen is a good way to use this heat otherwise lost).  Power plants rarely have max efficiency higher than 50%.)
Gas turbine can go higher. The best known efficiency for industrial  gas turbine is 60% ( still 40% energy lost)

Other energy losses,  thermal or mechanical, will add to the Carnot limit and the end , the efficiency of the power plant will be around 30% for coal and 40% for Natgas. It is  calculated as follows:

GHG emission as function of electricity produced

(7) according to  EIA:  The heat rates for electricity, i.e. the amount of fuel heat value required to produce electric energy.: ( in BTU/kWh, 1,000 BTU = 0.293 kWh) are:

Fuel(a) BTU/kWh(b) kWh(heat)/kWh(electric)(c) Efficiency % = 1/(b)
Natural Gas8,1522.3942

The table 4 means that:

  • Coal: only 33% of the energy contained in coal is transformed into electricity and 67% is lost.
  • NatGas: 42% of the energy contained in natural gas is transformed into electricity and 58% is lost. 

(8) CO2 emitted per unit of electricity can be calculated by multiplying  (6) by (7):

A (kgCO2/kWh heat ) x
B (kWh heat/kWh elec)
t CO2/ MWH
Coal0.357 x 3.060.9481
Natural Gas0.213 x 0.5080.5080.5

Table 5 indicates that the CO2 footprint of electricity produced by a gas-fired power plant is half the CO2 produced by a coal-fired power plant, representing a saving of 0.5 t per MWh.
That’s likely the basis for the claim that natural gas is clean. Although it still produces significant GHG emissions, bit less than coal?

But it that true? Not really…we still have to take into account fugitive emissions from natural gas.

GHG from Natural Gas Leakage

Fig2: NatGas with leakage vs coal
Fig2: NatGas with leakage vs coal

Natural gas leaks at various stage of its process:  Well heads, pipelines, valves, flanges, connections, compressors, etc,… How much exactly? it still debated (and likely difficult to assess due to the nature of ‘fugitive emissions’). We have seen that natural gas is mostly methane, a GHG with a GreenHouse Warming Potential (GWP) 72 times greater than CO2 (IPCC GWP), i.e. the emission of one kg of CH4 is the same as the emission of 72 kg of CO2 equivalent.

As shown above, the difference of CO2 emissions between nat gas  and coal is 500 kgCO2 per MWh electric. The GWP of 500 kg CO2 = 500/72 =  GWP of 6.11 kg CH4. It means that if 6.11 kg of gas is lost before it reaches the power plant, there will be no difference in total emissions between a gas-fired or a coal-fired power plant. At what leakage rate will that threshold happen?

(8) It can be calculated as follow::

  • Threshold of Methane leakage (500 kgCO2eq) 6.11 kgCH4
  • Specific heat of nat gas:(4) 12.94 kWh (heat) / kg(nat gas) – See (4) above
  • Heat rates: (7)  2.39 kWh(heat) / kWh(electricity) – See (7) above
  • dividing (7) by (4) is  2.39/12.94= 0.185 kg(nat gas)/kWh electricity or 184.67 kg(natGas)/MWh.
  • Leakage rate at the threshold is 6.11 / (184.67+6.11) =  3.21%.

EPA has estimated that this threshold equals 3.2 % . (EDF) confirming the above calculations.


Producing electricity with natural gas will not produce significantly less GHG per MWh than with coal (See Figure 2).   If the leakage is greater than  3.2%, then gas is worst than coal.

On a more positive note, if a natural gas plant is replaced by renewable energy (hydro, solar or wind), the renewables will displace almost 0.84 t of CO2 per MWh produced. (assuming the US EPA estimated general leakage rate of 2.4%)

Natural gas is not a solution to climate change, solar is.

Results Summaty
Results Summary